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You roll 2 fair dices with your eye closed, you are told "at least one of the dice is a one", what is the probability that the both dice are a 1?

 Dec 14, 2019
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When you roll the die, you know each die can show a number from 1 to 6, so there are 36 equally likely rolls.
Or: 6^2 = 36

 

We are told that at least one of the dice rolls is a 1. This means you can eliminate the possibilities that do not include a roll of 1. You can eliminate all but 11 cases, which are equally likely to occur:

 

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (3, 1), (4, 1), (5, 1), (6, 1)


In 10 out of the 11 cases, the other die shows a number other than 1. There is only 1 case–the (1, 1) roll–in which the both dice show a 1.

 

Therefore the probability is 1/11 {This is a question of conditional probability}.

 Dec 14, 2019

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